Answer
$\tan(\frac{x}{2})+\csc x=\frac{2-\cos x}{\sin x}$
Work Step by Step
Start with the left side:
$\tan(\frac{x}{2})+\csc x$
Use the identities $\tan(\frac{x}{2})=\frac{1-\cos x}{\sin x}$ and $\csc x=\frac{1}{\sin x}$:
$=\frac{1-\cos x}{\sin x}+\frac{1}{\sin x}$
Add the two fractions:
$=\frac{2-\cos x}{\sin x}$
Since this equals the right side, the identity is proven.